具有符号数学的矩阵给出了符号答案,而不是数值答案 [英] Matrix with symbolic math gives a symbolic answer, not a numeric one
问题描述
考虑以下矩阵
Ja(t1, t2, t3, t4, t5, t6) =
[ (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)) - sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/5 - sin(t1)/100 - (219*sin(t1)*sin(t2))/1000 - (19*cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 - (21*cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000 + (21*sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000, (219*cos(t1)*cos(t2))/1000 + (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)) - sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/5 - (19*cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 - (21*cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000 + (21*sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000, (sin(t5)*(cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) + cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 - (19*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100 - (21*cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, (sin(t5)*(cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) + cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 - (21*cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, -(cos(t5)*(cos(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) - sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5, 0]
[ cos(t1)/100 + (219*cos(t1)*sin(t2))/1000 + (29*cos(t1)*sin(t3))/1000 - (21*cos(t4)*(cos(t1)*sin(t3) - cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/1000 - (21*sin(t4)*(cos(t1)*cos(t3) + sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/1000 + (sin(t5)*(cos(t4)*(cos(t1)*sin(t3) - cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))) + sin(t4)*(cos(t1)*cos(t3) + sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))))/5 + (19*cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100, (219*cos(t2)*sin(t1))/1000 - (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) - sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 + (19*cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100 + (21*cos(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, (29*cos(t3)*sin(t1))/1000 - (21*cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 + (21*sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 - (19*sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 + (sin(t5)*(cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) - sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, (21*sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 - (21*cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 + (sin(t5)*(cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) - sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, (cos(t5)*(cos(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) + sin(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, 0]
[ 0, 0, (21*cos(t3)*cos(t4))/1000 - (29*cos(t3))/1000 - (21*sin(t3)*sin(t4))/1000 - (sin(t5)*(cos(t3)*cos(t4) - sin(t3)*sin(t4)))/5, (21*cos(t3)*cos(t4))/1000 - (21*sin(t3)*sin(t4))/1000 - (sin(t5)*(cos(t3)*cos(t4) - sin(t3)*sin(t4)))/5, -(cos(t5)*(cos(t3)*sin(t4) + cos(t4)*sin(t3)))/5, 0]
问题在于,当我输入参数时,MATLAB不会以数字方式计算矩阵,而是以符号形式将其留下.
这是结果:
Ja(q(1),q(2),q(3),q(4),q(5),q(6)) =
[ sin(63/100)/100 + (219*sin(528276371951843/1125899906842624)*sin(63/100))/1000 + (19*cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 + (sin(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000 - (21*sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000, (219*cos(528276371951843/1125899906842624)*cos(63/100))/1000 + (19*cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 + (sin(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000 - (21*sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000, - (19*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (sin(59/125)*(cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) + cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5 - (21*cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000, - (sin(59/125)*(cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) + cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5 - (21*cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000, -(cos(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5, 0]
[ cos(63/100)/100 + (219*sin(528276371951843/1125899906842624)*cos(63/100))/1000 + (29*cos(63/100)*sin(157/125))/1000 + (19*cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (21*cos(157/250)*(cos(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/1000 - (sin(59/125)*(cos(157/250)*(cos(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))) + sin(157/250)*(cos(63/100)*cos(157/125) + sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))))/5 - (21*sin(157/250)*(cos(63/100)*cos(157/125) + sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/1000, (19*cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (219*cos(528276371951843/1125899906842624)*sin(63/100))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000, (19*sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 - (29*cos(157/125)*sin(63/100))/1000 + (21*cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 - (21*sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 + (sin(59/125)*(cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))) - sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))))/5, (21*cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 - (21*sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 + (sin(59/125)*(cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))) - sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))))/5, -(cos(59/125)*(cos(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))) + sin(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))))/5, 0]
[ 0, 0, (21*cos(157/125)*cos(157/250))/1000 - (29*cos(157/125))/1000 - (21*sin(157/125)*sin(157/250))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250) - sin(157/125)*sin(157/250)))/5, (21*cos(157/125)*cos(157/250))/1000 - (21*sin(157/125)*sin(157/250))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250) - sin(157/125)*sin(157/250)))/5, -(cos(59/125)*(cos(157/125)*sin(157/250) + cos(157/250)*sin(157/125)))/5, 0]
有没有一种方法可以获取实数?
简短答案:使用eval
以数字方式评估符号表达式或使用 double
或符号与数字之间的转换 >
使用eval
是个不错的选择吗?
如Sardar Usama所指出的那样,使用eval
(用于评估字符串)通常是一种不好的做法:
但是,这是相同的eval
吗?
不,我不这么认为. help sym/eval
返回(与help eval
相反):
eval Evaluate a symbolic expression. eval(S) evaluates the character representation of the symbolic expression S in the caller's workspace.
还使用MATLAB调试器指出它是一个不同的函数.但是,完整的说明提到它会评估表达式的 character 表示形式,这也可以在源代码中看到:
s = evalin('caller',vectorize(map2mat(char(x))));
因此,它在内部使用类似于eval
的evalin
来评估字符串.这可能不是很有效.
所以,我们也应该避免使用sym/eval
吗?
也许不是,double
也在内部使用eval
来评估字符串:
Xstr = mupadmex('symobj::double', S.s, 0); X = eval(Xstr);
不同之处在于,sym/eval
使用eval
(evalin
)表示原始字符,即整个表达式,而double
使用它来解析最终结果,即数值评估值.
结论:对于您的示例,double
似乎是合适的方法,因为它的速度是使用eval
的速度的两倍.但是,对于以下示例,eval
稍快一些(〜15%):
my_function(x) = cos(x);
for i=2:100
my_function(x) = my_function(x) + cos(i*x);
end
Consider the following matrix
Ja(t1, t2, t3, t4, t5, t6) =
[ (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)) - sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/5 - sin(t1)/100 - (219*sin(t1)*sin(t2))/1000 - (19*cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 - (21*cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000 + (21*sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000, (219*cos(t1)*cos(t2))/1000 + (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)) - sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/5 - (19*cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 - (21*cos(t3)*cos(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000 + (21*sin(t3)*sin(t4)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/1000, (sin(t5)*(cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) + cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 - (19*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100 - (21*cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, (sin(t5)*(cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) + cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 - (21*cos(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*cos(t4)*sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, -(cos(t5)*(cos(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) - sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5, 0]
[ cos(t1)/100 + (219*cos(t1)*sin(t2))/1000 + (29*cos(t1)*sin(t3))/1000 - (21*cos(t4)*(cos(t1)*sin(t3) - cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/1000 - (21*sin(t4)*(cos(t1)*cos(t3) + sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/1000 + (sin(t5)*(cos(t4)*(cos(t1)*sin(t3) - cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))) + sin(t4)*(cos(t1)*cos(t3) + sin(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))))/5 + (19*cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100, (219*cos(t2)*sin(t1))/1000 - (sin(t5)*(cos(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)) - sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2))))/5 + (19*cos(t3)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/100 + (21*cos(t3)*cos(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000 - (21*sin(t3)*sin(t4)*(cos(t1)*cos(t2) - sin(t1)*sin(t2)))/1000, (29*cos(t3)*sin(t1))/1000 - (21*cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 + (21*sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 - (19*sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))/100 + (sin(t5)*(cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) - sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, (21*sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 - (21*cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))))/1000 + (sin(t5)*(cos(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) - sin(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, (cos(t5)*(cos(t4)*(sin(t1)*sin(t3) - cos(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1))) + sin(t4)*(cos(t3)*sin(t1) + sin(t3)*(cos(t1)*sin(t2) + cos(t2)*sin(t1)))))/5, 0]
[ 0, 0, (21*cos(t3)*cos(t4))/1000 - (29*cos(t3))/1000 - (21*sin(t3)*sin(t4))/1000 - (sin(t5)*(cos(t3)*cos(t4) - sin(t3)*sin(t4)))/5, (21*cos(t3)*cos(t4))/1000 - (21*sin(t3)*sin(t4))/1000 - (sin(t5)*(cos(t3)*cos(t4) - sin(t3)*sin(t4)))/5, -(cos(t5)*(cos(t3)*sin(t4) + cos(t4)*sin(t3)))/5, 0]
The problem is that when I put my arguments, MATLAB doesn't calculate the matrix numerically, rather it leaves it symbolically.
This is the result:
Ja(q(1),q(2),q(3),q(4),q(5),q(6)) =
[ sin(63/100)/100 + (219*sin(528276371951843/1125899906842624)*sin(63/100))/1000 + (19*cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 + (sin(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000 - (21*sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000, (219*cos(528276371951843/1125899906842624)*cos(63/100))/1000 + (19*cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 + (sin(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000 - (21*sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/1000, - (19*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (sin(59/125)*(cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) + cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5 - (21*cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000, - (sin(59/125)*(cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) + cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5 - (21*cos(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*cos(157/250)*sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000, -(cos(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5, 0]
[ cos(63/100)/100 + (219*sin(528276371951843/1125899906842624)*cos(63/100))/1000 + (29*cos(63/100)*sin(157/125))/1000 + (19*cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (21*cos(157/250)*(cos(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/1000 - (sin(59/125)*(cos(157/250)*(cos(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))) + sin(157/250)*(cos(63/100)*cos(157/125) + sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))))/5 - (21*sin(157/250)*(cos(63/100)*cos(157/125) + sin(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/1000, (19*cos(157/125)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/100 - (219*cos(528276371951843/1125899906842624)*sin(63/100))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)) - sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100))))/5 + (21*cos(157/125)*cos(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000 - (21*sin(157/125)*sin(157/250)*(cos(528276371951843/1125899906842624)*cos(63/100) + sin(528276371951843/1125899906842624)*sin(63/100)))/1000, (19*sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))/100 - (29*cos(157/125)*sin(63/100))/1000 + (21*cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 - (21*sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 + (sin(59/125)*(cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))) - sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))))/5, (21*cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 - (21*sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))))/1000 + (sin(59/125)*(cos(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))) - sin(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))))/5, -(cos(59/125)*(cos(157/250)*(sin(63/100)*sin(157/125) - cos(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100))) + sin(157/250)*(cos(157/125)*sin(63/100) + sin(157/125)*(cos(528276371951843/1125899906842624)*sin(63/100) - sin(528276371951843/1125899906842624)*cos(63/100)))))/5, 0]
[ 0, 0, (21*cos(157/125)*cos(157/250))/1000 - (29*cos(157/125))/1000 - (21*sin(157/125)*sin(157/250))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250) - sin(157/125)*sin(157/250)))/5, (21*cos(157/125)*cos(157/250))/1000 - (21*sin(157/125)*sin(157/250))/1000 + (sin(59/125)*(cos(157/125)*cos(157/250) - sin(157/125)*sin(157/250)))/5, -(cos(59/125)*(cos(157/125)*sin(157/250) + cos(157/250)*sin(157/125)))/5, 0]
Is there a way I can get real numbers ?
Short answer: evaluate your symbolic expression numerically using eval
or convert it to a specific type using one of these options, f.e. double
or vpa
.
Note that eval
may be twice as slow as using double
, but is sometimes slightly faster too
Explanation
The problem is that MATLAB does not evaluate your symbolic expression numerically, it only simplifies your expression mathematically.
Example:
syms x
my_function(x) = cos(x)
% exact algebraic solution is known:
my_function(0) % returns 1
my_function(pi) % returns -1
my_function(pi/2) % returns 0
my_function(pi/6) % returns 3^(1/2)/2
% result can only be numerically approximated:
my_function(3.1415) % returns cos(6283/2000)
my_function(1) % returns cos(1)
So, MATLAB is able to simplify the cos
expression when the result is exactly known. In general, the result of cos
can only be numerically evaluated, therefore MATLAB displays cos
in it answer.
If you want a numerical result you can use one of the following options:
eval
: evaluates your matrix numericallydouble
: converts to double precisionsingle
: converts to single precisionint8
: converts to 8 bit integers (alternativesint16
,int32
,int64
)vpa
: converts to variable-precision arithmetic, i.e. it allows you to specify the desired accuracy (number of significant digits) of the result
See Conversion Between Symbolic and Numeric for more information
Is using eval
a good option?
As pointed out by Sardar Usama, using eval
(to evaluate a string) is often bad practice:
But, is this the same eval
?
No, I don't think so. help sym/eval
returns (in contrast to help eval
):
eval Evaluate a symbolic expression. eval(S) evaluates the character representation of the symbolic expression S in the caller's workspace.
Also using the MATLAB debugger points out that it is a different function. However, the full explanation mentions that it evaluates the character representation of the expression, which can also be seen in the source code:
s = evalin('caller',vectorize(map2mat(char(x))));
So, it uses internally evalin
, which is similar to eval
, to evaluate a string. This may not be very efficient.
So, we should avoid sym/eval
too?
Maybe not, also double
uses eval
internally to evaluate a string:
Xstr = mupadmex('symobj::double', S.s, 0); X = eval(Xstr);
The difference is that sym/eval
uses eval
(evalin
) for the original character representation, i.e. the whole expression, whereas double
uses it to parse the final result, i.e. the numerically evaluated value.
Conclusion: for your example double
seems to be the appropriate method as it is twice as fast as using eval
. However, for the following example eval
is somewhat faster (~15%):
my_function(x) = cos(x);
for i=2:100
my_function(x) = my_function(x) + cos(i*x);
end
这篇关于具有符号数学的矩阵给出了符号答案,而不是数值答案的文章就介绍到这了,希望我们推荐的答案对大家有所帮助,也希望大家多多支持IT屋!